Primarily because of advances in VLSI technology, .DELTA..SIGMA. modulator based A/D converters have become popular in applications requiring high precision. [J. C. Candy and G. C. Temes, "Oversampling Methods for A/D and D/A Converters," Oversampling Delta-Sigma Data Converters Theory, Design and Simulations, edited by J. C. Candy and G. C. Temes, pp. 1-25, IEEE Press, New York 1992.]Although they employ complicated digital circuitry, their relatively simple analog circuitry tends to be robust with respect to component inaccuracies and noise. They generally do not require the trimmed components or precise reference voltages necessary in conventional A/D converters. Since fine-line VLSI technology is more amendable to high density, high speed digital circuitry than to accurate analog circuitry, .DELTA..SIGMA. modulator based converters are attractive candidates for VLSI implementation.
There are many types of .DELTA..SIGMA. modulators that may be used to implement the present invention. From a signal processing point of view, a large portion of them are special cases of an underlying generic system. An example is a second-order .DELTA..SIGMA. modulator system shown in FIG. 1 [Candy and Temes (1992), supra, p. 7] which satisfies the criteria of a generic system. The criteria are: (1) that it be an electronic system that operates on a discrete analog sequence and outputs a discrete time digital sequence at the same sample rate; (2) that the system contain quantizers; and (3) from a signal processing point of view, it has the property that if all quantizers are replaced by identity operators (e.g., wires), the output y(n) is related to the input x(n) as y(n)=x(n-L), where L is defined as the system delay, and when the quantizers are present the output is related to the input as y(n)=x(n-L)+e(n), where e(n) is a quantization error term.
A .DELTA..SIGMA. modulator based oversampling A/D converter is comprised of a .DELTA..SIGMA. modulator, a lowpass filter, and an N-sample decimator as shown in FIG. 2. The filter and decimator are together referred to as a decimation filter. Typically, the discrete-time analog input sequence corresponds to a continuous-time signal sampled at a rate Nf, where N is a positive integer referred to as the oversampling ratio and f is the Nyquist rate. This insures that the spectrum of the input sequence is restricted to ##EQU1## The decimation filter reduces the rate of the output sequence to f.
The main idea behind all the .DELTA..SIGMA. modulator variations is simple. In each system, the quantizers can be thought of as devices that add quantization noise sequences to their inputs. Since these sequences are injected into the system at the quantizer locations, they see a different filter configuration than the input sequence. The combination of filters is such that the input sequence is only delayed while the quantization noise sequences are highpass filtered. If the input sequence occupies the low frequency portion of the spectrum in which the quantization noise has been attenuated, subsequent lowpass decimation filtering can remove much of the remaining quantization noise without greatly distorting the input sequence. It is for this reason that .DELTA..SIGMA. modulators find application in oversampled A/D converters. Oversampling insures that the input sequence occupies only a low frequency portion of the spectrum, and decimation filtering removes the out-of-band quantization noise and reduces the output sample rate to the Nyquist rate.
The oversampling requirement is the essential drawback of .DELTA..SIGMA. modulator based converters; the circuitry must be designed to operate at a significantly higher rate than the system produces output samples. The greater the required accuracy of the A/D converted sequence, the larger the necessary oversampling ratio. Hence, accuracy is limited by circuit speed.
The proliferation of .DELTA..SIGMA. modulator architectures represents the continuing search for systems that require smaller oversampling ratios for a given level of accuracy. Most of the research has emphasized designing the filters and topology of the .DELTA..SIGMA. modulator to increase the frequency band over which the quantization noise is attenuated. Because of the nonlinearity introduced by the quantizers and the requirement that the topology of the system be amendable to VLSI implementation, this has proven to be a difficult problem. In particular, it is difficult to choose the architecture so as to minimize the required oversampling ratio while maintaining stability and a high tolerance to circuit imperfections.